The new downtown plan issued, if I recall correctly, earlier this year by the city specifically shows a Clinton Street subway veering off the Red Line at North/Clybourn and back on it again on the near South Side. This would have the benefit of connecting directly with Union and Ogilvie stations as well as providing probably a faster connection from the Red to the Blue/Green/Pink lines and vice versa. Perhaps the CTA is thinking in terms of doing Clinton Street first?
I think in practice the Clinton Street route probably should be done first. Circle Line won't work unless they have sufficient paths in the State Street tunnel during rush hour and the only way to achieve that is to find another place for Red Line trains to go. You could either have Red line trains alternating with Circle between State and Clinton, or move all Red Line trains to Clinton and run the Circle up the west side and down State.
